Math Snap

STEP 1

Assumptions1. The first side of the triangle is8m shorter than the second side.
. The third side is4 times as long as the first side.
3. The perimeter of the triangle is26m.
4. The lengths of the sides are positive real numbers.

STEP 2

Let's denote the sides of the triangle as follows- First side $x$ m- Second side $x +8$ m (since it's8m longer than the first side)
- Third side $4x$ m (since it's4 times the first side)

STEP 3

The perimeter of a triangle is the sum of the lengths of all its sides. So we can write the equation for the perimeter as follows$$x + (x +8) +x =26$$

STEP 4

implify the equation by combining like terms.
$$6x +8 =26$$

STEP 5

Subtract8 from both sides of the equation to isolate the term with $x$.
$$x =26 -8$$

STEP 6

Calculate the right side of the equation.
$$6x =18$$

STEP 7

Divide both sides of the equation by6 to solve for $x$.
$$x = \frac{18}{6}$$

STEP 8

Calculate the value of $x$.
$$x =3$$

STEP 9

Now that we have the value of $x$, we can find the lengths of the sides of the triangle.
- First side $x =3$ m- Second side $x +8 =3 +8$ m- Third side $4x =4 \times3$ m

Calculate the lengths of the second and third sides.
- Second side $3 +8 =$ m- Third side $4 \times3 =12$ mSo, the lengths of the sides of the triangle are3m,m, and12m.